Skip to main content
SpringerLink
Log in

Shear stress partitioning in large patches of roughness in the atmospheric inertial sublayer

  • Published:
Boundary-Layer Meteorology Aims and scope Submit manuscript

Abstract

Drag partition measurements were made in the atmospheric inertial sublayer for six roughness configurations made up of solid elements in staggered arrays of different roughness densities. The roughness was in the form of a patch within a large open area and in the shape of an equilateral triangle with 60 m long sides. Measurements were obtained of the total shear stress (τ) acting on the surfaces, the surface shear stress on the ground between the elements (τS) and the drag force on the elements for each roughness array. The measurements indicated that τS quickly reduced near the leading edge of the roughness compared with τ, and a τS minimum occurs at a normalized distance (x/h, where h is element height) of \(\approx -42\) (downwind of the roughness leading edge is negative), then recovers to a relatively stable value. The location of the minimum appears to scale with element height and not roughness density. The force on the elements decreases exponentially with normalized downwind distance and this rate of change scales with the roughness density, with the rate of change increasing as roughness density increases. Average τS : τ values for the six roughness surfaces scale predictably as a function of roughness density and in accordance with a shear stress partitioning model. The shear stress partitioning model performed very well in predicting the amount of surface shear stress, given knowledge of the stated input parameters for these patches of roughness. As the shear stress partitioning relationship within the roughness appears to come into equilibrium faster for smaller roughness element sizes it would also appear the shear stress partitioning model can be applied with confidence for smaller patches of smaller roughness elements than those used in this experiment.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Abbreviations

A f :

frontal area of roughness elements (m2)

A u :

unit area over which surface shear stress associated with a roughness element is distributed (m2)

b :

element breadth (m)

Cd :

surface drag coefficient

Cd e :

roughness element drag coefficient

Cd r :

rough surface drag coefficient

Cd s :

smooth surface drag coefficient

cv:

coefficient of variation

d :

displacement height (m)

F :

force on a roughness element (N)

g :

acceleration due to gravity (m s−2)

h :

element height (m)

IBL:

internal boundary layer

ISL:

inertial sublayer

m :

empirical constant between 0 and 1

n :

number of roughness elements occupying the ground area of the roughness array

NDD:

normalized downwind distance (x/h)

NED:

normalized element drag

R :

average friction velocity ratio

R l :

local friction velocity ratio at different positions in a roughness array

Re :

Reynolds number

R t :

threshold wind friction velocity ratio

SD:

standard deviation of a mean value

u :

wind speed (m s−1)

u * :

wind friction velocity (m s−1)

u * tR :

threshold wind friction velocity with roughness elements (m s−1)

u * tS :

threshold wind friction velocity of bare surface (m s−1)

x :

downwind distance (m)

z :

reference height above surface (m)

z w :

roughness sublayer height (m)

z o :

aerodynamic roughness length (m)

β:

ratio of element to surface drag coefficients

φm :

dimensionless wind speed gradient

κ:

von Kármán constant (0.4)

λ:

roughness density

μ:

molecular viscosity (N s m−2)

ρa :

air density (kg m−3)

σ:

roughness element basal area to frontal area ratio

τ:

total surface shear stress (N m−2)

τS :

surface shear stress on the area not covered by the roughness elements (N m−2)

τR :

surface shear stress attributed to the roughness elements (N m−2)

References

  • Bradley EF (1968). A micrometeorological study of velocity profiles and surface drag in the region modified by a change in surface roughness. Quart J Roy Meteorol Soc 94:361–379

    Google Scholar 

  • Cheng H, Castro IP (2002). Near wall flow over urban-like roughness. Boundary-Layer Meteorol 104:229–259

    Article  Google Scholar 

  • Crawley D, Nickling WG (2003). Drag partition for regularly-arrayed rough surfaces. Boundary-Layer Meteorol 107:445–468

    Article  Google Scholar 

  • Finnigan JJ (1979). Turbulence in waving wheat I. Mean statistics and honami. Boundary-Layer Meteorol 16:181–211

    Article  Google Scholar 

  • Garratt JR (1990). The internal boundary layer - a review. Boundary-Layer Meteorol 50:171–203

    Article  Google Scholar 

  • Gillette DA, Chen W (2001). Particle production and aeolian transport from a “supply-limited” source area in the Chihuahuan Desert, New Mexico, United States. J Geophys Res 106(D6):5267–5278

    Article  Google Scholar 

  • Gillette DA, Clayton RN, Mayeda TK, Jackson ML, Sridhar K (1978). Tropospheric aerosols from some major dust storms of the southwestern United States. J Appl Meteorol 17:832–845

    Article  Google Scholar 

  • Gillette D, Herrick J, Herbert G (2006). Wind characteristics of mesquite streets in the Northern Chihuahuan Desert, New Mexico, USA. Environ Fluid Mech 6(3):241–275

    Article  Google Scholar 

  • Gillies JA, Lancaster N, Nickling WG, Crawley D (2000). Field determination of drag forces and shear stress partitioning effects for a desert shrub (Sarcobatus vermiculatus, Greasewood. J Geophys Res Atmos 105(D20):24871–24880

    Article  Google Scholar 

  • Gillies JA, Nickling WG, King J (2002) Drag coefficient and plant form-response to wind speed in three plant species: Burning Bush (Euonymus alatus), Colorado Blue Spruce (Picea pungens glauca.), and Fountain Grass (Pennisetum setaceum). J Geophys Res Atmos 107(D24):10–1 – 10–15

    Google Scholar 

  • Gillies JA, Nickling WG, King J (2006) Aeolian sediment transport through large patches of roughness in the atmospheric inertial sublayer. J Geophys Res – Earth Surface 111, F02006, doi:10.1029/2005JF000434

  • Irwin HPAH (1980). A simple omnidirectional sensor for wind tunnel studies of pedestrian level winds. J Wind Eng Ind Aero 7:219–239

    Article  Google Scholar 

  • Jackson PS (1981). On the displacement height in the logarithmic velocity profile. J Fluid Mech 111:15–25

    Article  Google Scholar 

  • Kaimal JC, Finnigan JJ (1994) Atmospheric boundary layer flows: their structure and measurement. Oxford University Press, New York, 289 pp

  • King J, Nickling WG, Gillies JA (2005) Representation of vegetation and other non-erodible elements in aeolian shear stress partitioning models for predicting transport threshold. J Geophys Res – Earth Surface 110, F04015, doi:10.1029/2004JF000281

  • Kutzbach JE (1961) Investigations of the modification of wind profiles by artificially controlled surface roughness. In: Lettau HH (ed) Studies of the three-dimensional structure of the planetary boundary layer. pp 71–113

  • Lancaster N, Baas A (1998). Influence of vegetation cover on sand transport by wind: field studies at Owens Lake California. Earth Surf Process Landf 25:68–82

    Google Scholar 

  • Lettau HH (1969). Note on aerodynamic roughness parameter estimation on the basis of roughness element description. Appl Meteorol 8:828–832

    Article  Google Scholar 

  • Li A, Shao Y (2003). Numerical simulation of drag partition over rough surfaces. Boundary-Layer Meteorol 108:317–342

    Article  Google Scholar 

  • Luttmer C (2002) The partition of drag in salt grass communities. MS thesis, Guelph, Guelph, ON, Canada

  • Lyles L, Allison BE (1975). Wind erosion: Uniformly spacing nonerodible elements eliminates effects of wind direction variability. J Soil Water Conserv 30:225–226

    Google Scholar 

  • MacDonald RW, Griffiths RF, Hall DJ (1998). An improved method for the estimation of surface roughness of obstacle arrays. Atmos Environ 31(11):1857–1864

    Article  Google Scholar 

  • Malin MC, Carr MH, Danielson GE, Davies ME, Hartmann WK, Ingersoll AP, James PB, Masursky H, McEwen AS, Soderblom LA, Thomas P, Veverka J, Caplinger MA, Ravine MA, Soulanille TA, Warren JL (1998). Early views of the Martian surface from the Mars Orbiter Camera of Mars Global Surveyor. Science 279(5357):1681–1685

    Article  Google Scholar 

  • Marshall JK (1971). Drag measurements in roughness arrays of varying density and distribution. Agric Meteorol 8:269–292

    Article  Google Scholar 

  • Monteiro JP, Viegas DX (1996). On the use of Irwin and Preston wall shear stress probes in turbulent incompressible flows with pressure gradients. J Wind Eng Ind Aero 64:15–29

    Article  Google Scholar 

  • Musick HB, Gillette DA (1990) Field evaluation of relationships between a vegetated structural parameter and sheltering against wind erosion. Land Degrad Rehab 2:87–94

    Google Scholar 

  • Musick HB, Trujillo SM, Truman CR (1996). Wind-tunnel modelling of the influence of vegetation structure on saltation threshold. Earth Surf Process Landf 21(7):589–605

    Article  Google Scholar 

  • Okin GS, Gillette DA (2001). Distribution of vegetation in wind-dominated landscapes: Implications for wind erosion modeling and landscape processes. J Geophys Res 106(D9):9673–9683

    Article  Google Scholar 

  • Panofsky HA, Townsend AA (1964). Change of terrain roughness and the wind profile. Quart J Roy Meteorol Soc 90:147–155

    Google Scholar 

  • Rao KS, Wyngaard JC, Coté OR (1974). The structure of two-dimensional internal boundary layer over a sudden change of surface roughness. J Atmos Sci 31:738–746

    Article  Google Scholar 

  • Raupach MR (1992). Drag and drag partition on rough surfaces. Boundary-Layer Meteorol 60:375–395

    Article  Google Scholar 

  • Raupach MR, Gillette DA, Leys JF (1993). The effect of roughness elements on wind erosion threshold. J Geophys Res 98(D2):3023–3029

    Google Scholar 

  • Raupach MR, Thom AS, Edwards I (1980). A wind-tunnel study of turbulent flow close to regularly arrayed rough surfaces. Boundary-Layer Meteorol 18:373–397

    Article  Google Scholar 

  • Schlichting H (1936). Experimentelle untersuchungen zum rauhigkeitsproblem. Ingen – Arch 7:1–34

    Article  Google Scholar 

  • Taylor PA (1988) Turbulent wakes in the atmospheric boundary layer. In: Steffen WL, Denmead OT (eds) Flow and transport in the natural environment: advances and application. Springer-Verlag, Berlin, pp 270–292

  • Thom AS (1971). Momentum absorption by vegetation. Quart J Roy Meteorol Soc 97:414–428

    Article  Google Scholar 

  • Wieringa J (1993). Representative roughness parameters for homogeneous terrain. Boundary-Layer Meteorol 63:323–363

    Article  Google Scholar 

  • Wilson SA, Zimbelman JR (2004). Latitude-dependent nature and physical characteristics of transverse aeolian ridges on Mars. J Geophys Res 109:E10003, doi: 10.1029/2004JE002247

    Article  Google Scholar 

  • Wolfe SA, Nickling WG (1996). Shear stress partitioning in sparsely vegetated desert canopies. Earth Surf Process Landf 21:607–619

    Article  Google Scholar 

  • Wooding RA, Bradley EF, Marshall JK (1973) Drag due to regular arrays of roughness elements of varying geometry. Boundary-Layer Meteorol 5:285–308

    Article  Google Scholar 

  • Wu H, Stathopoulos T (1994). Further experiments on Irwin’s surface wind sensor. J Wind Eng Ind Aero 53:441–452

    Article  Google Scholar 

  • Wyatt V, Nickling WG (1997). Drag and shear stress partitioning in sparse desert creosote communities. Can J Earth Sci 34:1486–1498

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Particle Emissions Measurement Laboratory, Division of Atmospheric Sciences, Desert Research Institute, 2215 Raggio Parkway, Reno, NV, 89512, USA

    John A. Gillies

  2. Wind Erosion Laboratory, Department of Geography, University of Guelph, Guelph, ON, N1G 2W1, Canada

    William G. Nickling & James King

Authors
  1. John A. Gillies
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. William G. Nickling
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. James King
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to John A. Gillies.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gillies, J.A., Nickling, W.G. & King, J. Shear stress partitioning in large patches of roughness in the atmospheric inertial sublayer. Boundary-Layer Meteorol 122, 367–396 (2007). https://doi.org/10.1007/s10546-006-9101-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10546-006-9101-5

Keywords

Search

Navigation